Clojureで多次元配列

ClojureでJavaの配列を利用して数値計算を扱う。

Transcript

1. @ichisemasashi 2020೥12݄23೔ ClojureͰଟ࣍ݩ഑ྻ
2. ࠷ۙؾ෇͍ͨɺࣗ෼͕ίϯϐϡʔλʔͰ΍Γ͔ͨͬͨ͜ͱ => ʮ਺஋ܭࢉʯ - ͱΓ͋͑ͣɺJuliaΛ࢖ͬͯษڧΛ͍͕ͯͨ͠ɺͰ͖Ε͹ClojureͰษڧ Λ͔ͨͬͨ͠ɻ - Ͱ΋Clojureʹ͸ଟ࣍ݩ഑ྻ͕ͳ͍ͱࢥ͍ͬͯͨɻ -> Javaͷ഑ྻΛ࢖͑͹ྑ͍ɻ -> tnoda͞ΜͷʮJava ͷ഑ྻΛར༻ͯ͠ϝϞϦͱ࣌ؒͷนΛಥ ഁ͢ΔɽʯʹɺJavaͷ഑ྻͷ࢖͍ํ͕੔ཧ͞Ε͍ͯͨɻ
3. ClojureͰJavaͷ഑ྻΛར༻͢Δ ഑ྻͷੜ੒ user=> (def my-array (make-array Integer/TYPE 2 2)) #'user/my-array
4. ClojureͰJavaͷ഑ྻΛར༻͢Δ ഑ྻͷදࣔ user=> (pprint my-array) [[0, 0], [0, 0]] nil
5. ClojureͰJavaͷ഑ྻΛར༻͢Δ ഑ྻͷཁૉΛࢀর user=> (aget ^ints my-array 0 0) 0
6. ClojureͰJavaͷ഑ྻΛར༻͢Δ ഑ྻͷཁૉʹσʔλΛઃఆ user=> (aset ^ints my-array 0 0 (int 100)) 100 user=> (aget ^ints my-array 0 0) 100 user=> (pprint my-array) [[100, 0], [0, 0]] nil
7. ࣮૷ྫɿΨ΢ε-βΠσϧ๏ʹΑΔ࿈ཱ1࣍ํఔࣜͷղ๏ Ψ΢ε-βΠσϧ๏ͷ֓ཁ 5x + y + z = 10 x + 4y + z = 12 2x + y + 3z = 13 }
8. ࣮૷ྫɿΨ΢ε-βΠσϧ๏ʹΑΔ࿈ཱ1࣍ํఔࣜͷղ๏ Ψ΢ε-βΠσϧ๏ͷ֓ཁ 5x + y + z = 10 x + 4y + z = 12 2x + y + 3z = 13 } x = (10 − y − z)/5 y = (12 − x − z)/4 z = (13 − 2x − y)/3 }
9. ࣮૷ྫɿΨ΢ε-βΠσϧ๏ʹΑΔ࿈ཱ1࣍ํఔࣜͷղ๏ Ψ΢ε-βΠσϧ๏ͷ֓ཁ 5x + y + z = 10 x + 4y + z = 12 2x + y + 3z = 13 } x = (10 − y − z)/5 y = (12 − x − z)/4 z = (13 − 2x − y)/3 } x y z ॳظ஋ 1 1 1 1८໨ 1.600 2.350 2.483 2८໨ 1.033 2.121 2.938 3८໨ 0.988 2.019 3.002 4८໨ 0.996 2.001 3.002 5८໨ 0.999 1.999 3.001
10. ࣮૷ྫɿΨ΢ε-βΠσϧ๏ʹΑΔ࿈ཱ1࣍ํఔࣜͷղ๏ Ψ΢ε-βΠσϧ๏ͷ࣮૷ (def an-eq (make-array Double/TYPE 3 4)) (def N (alength an-eq)) (defn set-eq [arr n x y z w] (aset ^doubles arr n 0 (double x)) (aset ^doubles arr n 1 (double y)) (aset ^doubles arr n 2 (double z)) (aset ^doubles arr n 3 (double w))) (set-eq an-eq 0 5 1 1 10) (set-eq an-eq 1 1 4 1 12) (set-eq an-eq 2 2 1 3 13) (pprint an-eq)
11. ࣮૷ྫɿΨ΢ε-βΠσϧ๏ʹΑΔ࿈ཱ1࣍ํఔࣜͷղ๏ Ψ΢ε-βΠσϧ๏ͷ࣮૷(ଓ) (def res-arr (make-array Double/TYPE 3)) (dotimes [i N] (aset ^doubles res-arr i (double 1))) (pprint res-arr) (def tmp-arr (make-array Double/TYPE 3)) (pprint tmp-arr) (defn eq-elm [x y] (aget ^doubles an-eq x y)) (defn res-elm [x] (aget ^doubles res-arr x)) (defn tmp-elm [x] (aget ^doubles tmp-arr x))
12. ࣮૷ྫɿΨ΢ε-βΠσϧ๏ʹΑΔ࿈ཱ1࣍ํఔࣜͷղ๏ Ψ΢ε-βΠσϧ๏ͷ࣮૷(ଓ) (def MAX_LOOP 30) (def EPS (double 0.0001)) (def q (atom (double 1.0))) (def ll (atom 0)) (defn display-result [] (dotimes [i N] (let [res (res-elm i)] (println (format "x%d = %9.6f" i res)))))
13. ࣮૷ྫɿΨ΢ε-βΠσϧ๏ʹΑΔ࿈ཱ1࣍ํఔࣜͷղ๏ Ψ΢ε-βΠσϧ๏ͷ࣮૷(ଓ) (defn computing [] (let [s (atom (double 0.0))] (dotimes [i N] (reset! s (double 0.0)) (dotimes [j N] (if (not= i j) (reset! s (+ @s (* (eq-elm i j) (res-elm j)))))) (aset ^doubles tmp-arr i (/ (- (eq-elm i N) @s) (eq-elm i i))) (reset! q (+ @q (Math/abs (- (res-elm i) (tmp-elm i))))) (aset ^double res-arr i (tmp-elm i)))))
14. ࣮૷ྫɿΨ΢ε-βΠσϧ๏ʹΑΔ࿈ཱ1࣍ํఔࣜͷղ๏ Ψ΢ε-βΠσϧ๏ͷ࣮૷(ଓ) (while (and (< EPS @q) (>= MAX_LOOP @ll)) (do (swap! ll inc) (reset! q (double 0.0)) (computing))) (if (>= @ll MAX_LOOP) (println "ऩଋͤͣɻ") (display-result))